Cyril of Alexandria

They used to sacrifice goats for sin; for this reason the sacrifice was called sin. By offering a goat on the altar, the priests at the right time used to bring the intestines and the lard, and they ate the rest. This was ordered by the divine law. … "They eat the sins of my people" means they eat the offerings brought for sins.

Commentary On Hosea 3:40 ↗

Jerome

"they will eat the sins of my people, and lift up their souls to their iniquity." LXX: "they will eat the sins of my people, and receive them in their iniquities; others their souls." For indeed, the priests eat the sins of my people, concerning whom it is written: "Those who devour my people, like bread" (Ps 13:8). And therefore they eat the sins of my people, consenting to the crimes of wrongdoers since, when they witness them sinning, not only do they not rebuke them, but they praise and exalt them and call them blessed. …

Commentary on Hosea 4:7-9 ↗

Gregory the Dialogist

But we must remember without ceasing what is written about certain ones: They shall eat the sins of my people. Why are they said to eat the sins of the people, unless because they encourage the sins of transgressors, lest they lose their temporal payments? But we also who live from the offerings of the faithful, which they offered for their sins, if we eat and remain silent, we without doubt eat their sins. Let us consider, therefore, what a crime it is before God to eat the price of sins and to do nothing against sins by preaching.

Forty Gospel Homilies, Homily 17 ↗